We propose a polynomial-time decision procedure for hereditary history preserving bisimilarity (hhp-b) on Basic Parallel Processes
(BPP). Furthermore, we give a sound and complete equational axiomatization for the equivalence. Both results are derived from
a decomposition property of hhp-b, which is the main technical contribution of the paper. Altogether, our results complement
previous work on complexity and decomposition of classical and history-preserving bisimilarity on BPP.
This work is supported by the European Community Research Training Network Games.